Bernoulli's principle relates the pressure of a fluid to its elevation and its speed. Bernoulli's equation can be used to approximate these parameters in water, air or any fluid that has very low viscosity. Students learn about the relationships between the components of the Bernoulli equation through real-life engineering examples and practice problems.
Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standard Network (ASN), a project of JES & Co. (www.jesandco.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
Click on the standard groupings to explore this hierarchy as it applies to this document.
- Colorado: Math
- a. Represent, solve, and interpret problems in various contexts using linear, quadratic, and exponential functions (Grades 9 - 12)  ...show
- Colorado: Science
- a. Develop, communicate, and justify an evidence-based scientific explanation regarding the potential and kinetic nature of mechanical energy (Grades 9 - 12)  ...show
- b. Use appropriate measurements, equations and graphs to gather, analyze, and interpret data on the quantity of energy in a system or an object (Grades 9 - 12)  ...show
- Common Core State Standards for Mathematics: Math
- 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. (Grades 9 - 12)  ...show
- 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (Grades 9 - 12)  ...show
- International Technology and Engineering Educators Association: Technology
- Next Generation Science Standards: Science
- Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. (Grades 9 - 12)  ...show
- Calculate an unknown fluid condition (for example, fluid pressure, velocity, density or height) at one point along a flow streamline, if conditions are known at another point along the same streamline.
- Use the Bernoulli equation to explain that faster airflow causes a decrease in pressure, and give an example of a real-life application.
Lesson Background and Concepts for Teachers
|Bernoulli Principle:||In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Named after Dutch-Swiss mathematician Daniel Bernoulli who published his principle in his book Hydrodynamica in 1738. Also called the Bernoulli effect.|
|inviscid flow:||Flow in which one can ignore the effects of fluid viscosity.|
|streamline:||A line tangent to the flow of a fluid at any given instant.|
|Venturi effect:||The reduction in fluid pressure that results when a fluid flows through a constricted section of pipe. As a fluid's velocity increases, its pressure decreases, and vice versa. Named after Italian physicist Giovanni Battista Venturi (1746–1822).|
- A Shot Under Pressure - Students use their understanding of projectile physics and fluid dynamics to find the water pressure in a water gun. By measuring the range of the water jet, they are able to calculate the theoretical pressure. Students create graphs to analyze how the predicted pressure relates to the number of times they pump the powerful squirt gun.
- Bernoulli Equation Practice Worksheet (doc)
- Bernoulli Equation Practice Worksheet (pdf)
- Bernoulli Equation Practice Worksheet Answers (doc)
- Bernoulli Equation Practice Worksheet Answers (pdf)
- Bernoulli Flow Graphics (suitable for overhead transparencies or handouts) (ppt)
- Bernoulli Flow Graphics (suitable for overhead transparencies or handouts) (pdf)
Lesson Summary Assessment
Additional Multimedia Support
Bernoulli's principle (definition). Last updated February 11, 2010. Wikipedia, The Free Encyclopedia. Accessed February 17, 2010. http://en.wikipedia.org/w/index.php?title=Bernoulli%27s_principle&oldid=343435891
Knight, Randall. Physics for Scientists and Engineers: a Strategic Approach. Second edition. San Francisco, CA: Pearson Addison-Wesley, 2008.
Munson, B. R., Young, D.F., Okiishi, T.H. Fundamentals of Fluid Mechanics. Fifth edition. New York, NY: John Wiley & Sons, Inc., 2006.
Venturi effect (definition). Last updated February 12, 2010. Wikipedia, The Free Encyclopedia. Accessed February 17, 2010. http://en.wikipedia.org/w/index.php?title=Venturi_effect&oldid=343508711
James Prager, Karen King, Denise W. Carlson
© 2009 by Regents of the University of Colorado.
Integrated Teaching and Learning Program and Laboratory, College of Engineering, University of Colorado Boulder
Last modified: April 1, 2015